Weak Convergence and Rate of Convergence of MIMO Capacity Random Variable

Abstract

Recent works on the distribution function of the capacity of independent and identically distributed (i.i.d.) and semicorrelated narrowband channels show that the outage capacity computed using a Gaussian approximation is close to the true outage capacity even for few antennas. Motivated by physical scattering considerations, we study a multi-antenna channel model with independent entries that are not necessarily identically distributed and show the weak convergence of capacity to a Gaussian random variable. The channel model considered in this paper subsumes well-studied cases like the i.i.d. and separable correlation models and thus we generalize previous results on weak convergence of multi-antenna capacity. Using recent results from random matrix theory, we also study the rate of convergence of ergodic capacity of i.i.d. channels to its limit value. Employing a well-known conjecture from random matrix theory, we establish tight results for the rate of convergence and show a dependence of this rate on signal-to-noise ratio